Background for the Question
A common understanding is that translating poetry from one language to another is essentially impossible to accomplish without much compromise. The current Wikipedia article (as of 9/24/2016) on Untranslatability states of poetry:
The two areas which most nearly approach total untranslatability are poetry and puns; poetry is difficult to translate because of its reliance on the sounds (for example, rhymes) and rhythms of the source language;
And the famous statement of Robert Frost is quoted in the Wikiquote article on Poetry:
I could define poetry this way: it is that which is lost out of both prose and verse in translation ... Conversations on the Craft of Poetry (1959); often quoted as "Poetry is what gets lost in translation".
Generally speaking, the problem is either that the meaning is retained, but rhyme and rhythm lost, or an attempt to maintain the latter compromises the former.
Now in Tolkien's works, the English of our text often has the rhyme and rhythm, which implies the meaning is probably not retained well. If this were true for one instance, that might be explained. But instead, the rhyme and rhythm happens regularly, and from various languages, many times actually representing two levels of translation, since the Common Speech is not English.
For purposes here, I've just taken a short sampling from three languages in The Two Towers, but similar things could be stated of other portions.
Common Speech (apparently) to English ("The Departure of Boromir", The Two Towers, first four verses only as a representative example)
Through Rohan over fen and field where the long grass grows
The West Wind comes walking, and about the walls it goes.
'What news from the West, O wandering wind, do you bring to me tonight?
Have you seen Boromir the Tall by moon or by starlight?
Analysis: There is two forms of rhyming at the ends of these verses, alliteration of 'f' and 'w', with a sophisticated rhythm apparent in verse 2 and 3 with the 'w' sound where it forms a symmetrical pattern with the other words:
W W - W - - - W - - W - - - W - W W
Note that if one looked at the rest of the verses in that passage, other rhyme and rhythm points could easily be noted.
(Ancient) Elvish to Common Speech to English ("Treebeard", The Two Towers, first six verses; that it is Elvish comes from Treebeard's testimony after the verses):
Learn now the lore of Living Creatures!
First name the four; the free peoples:
Eldest of all, the elf-children;
Dwarf the delver, dark are his houses;
Ent the earthborn, old as mountains;
Man the mortal, master of horses:
Analysis: There is a lot going on in this short section, so much it made no sense to bold the words, as most would be.
There is a complicated alliteration in the first two verses of 'L' and 'F' respectively, as it also includes a sophisticated parallel rhythm between the lines (using the 2nd and 3rd words to match sounds also), and then a rhyme of the last word (here represented by an X; which rhyme also matches lines 4-6 of the other free peoples than the Elves who made the "old lists"):
L n t L - L X
F n t F - F X
Lines 4-6 each have an alliteration of the 1st and 3rd word, and then lines 4 and 6 match the same alliteration with the 4th word, the break occurring in line 5 with the Ents (since "Ent" and "old" are not alliterated), which is who the lists were made for by the elves. So the patterns in these verses are (still with X showing the continued rhyme from verses 1 and 2):
D t D, D - - X
E t E, - - X
M t M, M - X
The 3rd line about the first of the free peoples, the Elves, is the most unique in form, yet it has an alliterative scheme of its first and last words ("el"), while its 3rd word ("all") rhymes with the 3rd word ("mortal") of the fourth of the four peoples, Men (which, speculatively, is interesting, since the Elves can choose to become mortal, similar to men, and procreate with men).
The later song from the Elves about the Entwives has just as much sophistication of rhyme, alliteration, etc.
Language of Rohirrim to Common Speech to English ("The King of the Golden Hall", The Two Towers, all verses):
Where now the horse and the rider? Where is the horn that was blowing?
Where is the helm and the hauberk, and the bright hair flowing?
Where is the hand on the harpstring, and the red fire glowing?
Where is the spring and the harvest and the tall corn growing?
They have passed like rain on the mountain, like a wind in the meadow:
The days have gone down in the West behind the hills into shadow.
Who shall gather the smoke of the dead wood burning,
Or behold the flowing years from the Sea returning?
Analysis: There is a large amount of apparently intentional alliteration of the letter 'h' in these verses, and then two forms of rhyming at the ends of the verses.
So from an out-of-universe explanation, it is clear Tolkien intended to showcase good (English) poetry in his books and also to give meaning to those. That is, obviously the verses above were written with the meaning Tolkien wanted with the rhyme and rhythm working in the English language.
But what I want to know is if Tolkien, in any of his writings, ever gave an in-universe explanation on how those poems and songs could come to be translated into the Common Speech (in the case of from Elvish or Rohirrim) and from that, into English, with both the meaning and the form (rhyme, rhythm, etc.) so well intact?